A new fractional derivative operator and applications
نویسندگان
1 Department of Mathematics, Faculty of Science Tetouan, Abdelmalek Essaad University, Tetouan, Morocco
2 Department of Mathematics, Faculty of Science Tetouan, Abdelmalek Essaad University, Tetouan, Morocco
3 Department of Mathematics, Faculty of Science Tetouan, Abdelmalek Essaad University, Tetouan, Morocco
doi
10.22075/ijnaa.2022.26841.3423چکیده
We introduce a new fractional derivative which obeys classical properties including linearity, product rule, power rule, vanishing derivatives for constant functions, chain rule, quotient rule, Rolle's Theorem and the Mean Value Theorem:$$D^\alpha(f)(t)=\lim _{\epsilon \rightarrow 0} \frac{f\left(t e^{\frac{1}{\Gamma(1-\alpha)}} e^{-\alpha}\right)-f(t)}{\epsilon},$$this definition is comfortable with the classical definition of the Caputo Fractional Operator.
